Vibrating beam force transducers are often used as force-to-frequency converters in accelerometers and other instruments. In one known arrangement, the transducers are used in push-pull pairs in which a given acceleration or force will put one transducer in compression and the other in tension. This mode of operation provides a high degree of compensation for many common mode errors, i.e., errors that cause the frequencies of the transducers to shift by the same amount in the same direction, because the shifts cancel in the algorithms normally used to process the transducer outputs. Such errors include vibration rectification errors, changes induced by temperature change, most aging errors, and measurement errors induced by a drift in the clock frequency.
To obtain a high rejection of common mode errors, a pair of force transducers should be as similar as possible to one another, so that their responses to error sources such as temperature change and aging are as similar as possible to one another. For example, when the transducers are fabricated from crystalline quartz, the transducers are often etched from adjacent positions on a quartz wafer. However, when two transducers are used on a common structure, e.g., two transducers attached to a single accelerometer proof mass, another consideration intrudes. When the transducers are well matched, there will be conditions within the operating range of the instrument where both transducers vibrate at the same frequency, leading to the possibility of a "lock in" condition and a consequent local nonlinearity that may produce errors in the output of the instrument.